Abstract
We study the boundedness and compactness of generalized Toeplitz operators with locally integrable symbols on Bergman spaces where is a bounded simply connected domain with smooth boundary. We give sufficient conditions for boundedness and compactness of in terms of “averages” of symbol a over certain Cartesian squares. The main tool in the proof is the Whitney covering: is decomposed into union of countably many squares whose side lengths are comparable to the boundary distance. If a is nonnegative, we show that the given conditions are also necessary.
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